How long will it take you to double your principal in an account that pays 6.5% annual interest compounded continuously
+128406
We have
2P = Pe^(r * t ) where r = .065 and t is the time to double
2P = Pe^( .065 * t) divide both sides by P
2 = e^(.065 * t ) take the Ln of both sides
Ln 2 = Ln 2^(.065 * t) and by a log property we can write
Ln 2 = ( .065 * t) Ln e and Ln e = 1 so we can disregard this
Ln 2 = .065 * t divide both sides by .065
Ln 2 / . 065 = t ≈ 10.7 years
